List two ways that calculating angles is useful to you?

It states that 'when a triangle has a right angle then the sum of squares of the horizontal and vertical sides is same as the square of the hypotenuse'.

i.e. [tex]hypotenuse^{2} =horizontal^{2} +vertical^{2}[/tex]

Further, this theorem is used in many real life situations such as architecture, construction, navigation and many more.

For e.g. We need to find the shortest path in the figure 1 below to reach from C to A. Here, either we can go through CB to BA or take the route CA by finding the distance to cover using Pythagorus Theorem.

i.e. [tex]CA^{2} =CB^{2} +BA^{2}[/tex]

i.e. i.e. [tex]CA^{2} =40^{2} +30^{2}[/tex]

i.e. [tex]CA^{2} =2500[/tex]

i.e. [tex]CA =50[/tex]

So, the shortest distance to reach A from C will be 50 m.

2. SOHCAHTOA

This terms represents to the trigonometric form of the angles of a right triangle given by,

[tex]\sin \theta = \frac{opposite}{hypotenuse}[/tex]

[tex]\cos \theta = \frac{adjacent}{hypotenuse}[/tex]

[tex]\tan\theta = \frac{opposite}{adjacent}[/tex]

Further, these relations are used in many real life situations such as measuring the height of monuments, to know the angles for roof inclinations, in physics, marine engineering and many more.

For e.g. If we want to find the angles between the boat and shark in the figure 2, we have,

[tex]\cos x = \frac{30}{50}[/tex] i.e. [tex]\cos x = 0.6[/tex] i.e. [tex]x=\arctan 0.6[/tex] i.e. [tex]x=0.54[/tex]

Hence, we see that calculating angles are useful in real life situations.